Dynamic connectivity and path formation time in Poisson networks
The connectivity of wireless networks is commonly analyzed using static geometric graphs. However, with half-duplex radios and due to interference, static or instantaneous connectivity cannot be achieved. It is not necessary, either, since packets take multiple time slots to propagate through the network. For example, if a packet traverses a link in one time slot, it is irrelevant if the next link is available in that time slot also, but it is relevant if the next hop exists in the next time slot. To account for half-duplex constraints and the dynamic changes in the transmitting set of nodes due to MAC scheduling and traffic loads, we introduce a random multi-digraph that captures the evolution of the network connectivity in a dynamic fashion. To obtain concrete results, we focus on Poisson networks, where transmitters form a Poisson point process on the plane at all time instants. We first provide analytical results for the degree distribution of the graph and derive the distributional properties of the end-to-end connection delay using techniques from first-passage percolation and epidemic processes. Next, we prove that under some assumptions, the delay scales linearly with the source–destination distance even in the presence of interference. We also provide simulation results in support of the theoretical results.
KeywordsAd hoc networks Connectivity Interference Delay Percolation
The partial support of the NSF (grants CNS 1016742 and CCF 1216407) and the DARPA/IPTO IT-MANET program (grant W911NF-07-1-0028) is gratefully acknowledged.
- 2.Aldous, D., & Steele, J. (2003). In H. Kesten (Ed.) Probability on discrete structures (Encyclopaedia of mathematical sciences (Vol. 110)). Springer.Google Scholar
- 3.Baccelli, F., & Blaszczyszyn, B. (2009). Stochastic geometry and wireless networks, part II: Applications. Hanover: Now Publishers Inc.Google Scholar
- 6.Dousse, O., Mannersalo, P., & Thiran, P. (2004). Latency of wireless sensor networks with uncoordinated power saving mechanisms. In Proceedings of the 5th ACM international symposium on mobile ad hoc networking and computing (pp. 109–120).Google Scholar
- 8.Ganti, R., & Haenggi, M. (2007). Dynamic connectivity and packet propagation delay in ALOHA wireless networks. In Forty-first asilomar conference on signals, systems and computers. (ACSSC 2007) (pp. 143–147). IEEEGoogle Scholar
- 9.Ganti, R., & Haenggi, M. (2009) Bounds on information propagation delay in interference-limited ALOHA networks. In Workshop on spatial stochastic models for wireless networks (SPASWIN) Google Scholar
- 15.Hammersley, J., & Welsh, D. (1965) First-passage percolation, subadditive processes, stochastic networks, and generalized renewal theory. Bernoulli–Bayes–Laplace anniversary volume (pp. 61–110).Google Scholar
- 20.Kong, Z., & Yeh, E. (2009). Connectivity, percolation, and information dissemination in large-scale wireless networks with dynamic links. Arxiv preprint arXiv:0902.4449Google Scholar
- 21.Kumar, P., & Xue, F. (2006) . Scaling laws for ad-hoc wireless networks: An information theoretic approach. Hanover: Now Publishers Inc.Google Scholar